Vol. 311, No. 2, 2021

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Spinoriality of orthogonal representations of $\mathrm{GL}_n(\mathbb{F}_q)$

Rohit Joshi and Steven Spallone

Vol. 311 (2021), No. 2, 369–383
Abstract

We determine which orthogonal representations V of GLn(𝔽q) lift to the double cover Pin(V ) of the orthogonal group O(V ). We cover all n 1 and prime powers q, except for (n,q) = (3,4).

Keywords
orthogonal representations, spinoriality, finite groups of Lie type
Mathematical Subject Classification
Primary: 20G05
Secondary: 20G40
Milestones
Received: 15 August 2020
Revised: 29 December 2020
Accepted: 13 January 2021
Published: 31 July 2021
Authors
Rohit Joshi
Bhaskaracharya Pratishthan
Pune
India
Steven Spallone
IISER Pune
Pune
India